Before Calculus | p. 1 |
Functions | p. 1 |
New Functions from Old | p. 15 |
Families of Functions | p. 27 |
Inverse Functions | p. 38 |
Limits And Continuity | p. 49 |
Limits (An Intuitive Approach) | p. 49 |
Computing Limits | p. 62 |
Limits at Infinity; End Behavior of a Function | p. 71 |
Limits (Discussed More Rigorously) | p. 81 |
Continuity | p. 90 |
Continuity of Trigonometric Functions | p. 101 |
The Derivative | p. 110 |
Tangent Lines and Rates of Change | p. 110 |
The Derivative Function | p. 122 |
Introduction to Techniques of Differentiation | p. 134 |
The Product and Quotient Rules | p. 142 |
Derivatives of Trigonometric Functions | p. 148 |
The Chain Rule | p. 153 |
Implicit Differentiation | p. 161 |
Related Rates | p. 168 |
Local Linear Approximation; Differentials | p. 175 |
The Derivative In Graphing And Applications | p. 187 |
Analysis of Functions I: Increase, Decrease, and Concavity | p. 187 |
Analysis of Functions II: Relative Extrema; Graphing Polynomials | p. 197 |
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents | p. 207 |
Absolute Maxima and Minima | p. 216 |
Applied Maximum and Minimum Problems | p. 224 |
Rectilinear Motion | p. 238 |
Newton's Method | p. 246 |
Rolle's Theorem; Mean-Value Theorem | p. 252 |
Integration | p. 265 |
An Overview of the Area Problem | p. 265 |
The Indefinite Integral | p. 271 |
Integration by Substitution | p. 281 |
The Definition of Area as a Limit; Sigma Notation | p. 287 |
The Definite Integral | p. 300 |
The Fundamental Theorem of Calculus | p. 309 |
Rectilinear Motion Revisited Using Integration | p. 322 |
Average Value of a Function and its Applications | p. 332 |
Evaluating Definite Integrals by Substitution | p. 337 |
Applications Of The Definite Integral In Geometry, Science, And Engineering | p. 347 |
Area Between Two Curves | p. 347 |
Volumes by Slicing; Disks and Washers | p. 355 |
Volumes by Cylindrical Shells | p. 365 |
Length of a Plane Curve | p. 371 |
Area of a Surface of Revolution | p. 377 |
Work | p. 382 |
Moments, Centers of Gravity, and Centroids | p. 391 |
Fluid Pressure and Force | p. 400 |
Exponential, Logarithmic, And Inverse Trigonometric Functions | p. 409 |
Exponential and Logarithmic Functions | p. 409 |
Derivatives and Integrals Involving Logarithmic Functions | p. 420 |
Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions | p. 427 |
Graphs and Applications Involving Logarithmic and Exponential Functions | p. 434 |
L'Hôpital's Rule; Indeterminate Forms | p. 441 |
Logarithmic and Other Functions Defined by Integrals | p. 450 |
Derivatives and Integrals Involving Inverse Trigonometric Functions | p. 462 |
Hyperbolic Functions and Hanging Cables | p. 472 |
Principles Of Integral Evaluation | p. 488 |
An Overview of Integration Methods | p. 488 |
Integration by Parts | p. 491 |
Integrating Trigonometric Functions | p. 500 |
Trigonometric Substitutions | p. 508 |
Integrating Rational Functions by Partial Fractions | p. 514 |
Using Computer Algebra Systems and Tables of Integrals | p. 523 |
Numerical Integration; Simpson's Rule | p. 533 |
Improper Integrals | p. 547 |
Mathematical Modeling With Differential Equations | p. 561 |
Modeling with Differential Equations | p. 561 |
Separation of Variables | p. 568 |
Slope Fields; Euler's Method | p. 579 |
First-Order Differential Equations and Applications | p. 586 |
Infinite Series | p. 596 |
Sequences | p. 596 |
Monotone Sequences | p. 607 |
Infinite Series | p. 614 |
Convergence Tests | p. 623 |
The Comparison, Ratio, and Root Tests | p. 631 |
Alternating Series; Absolute and Conditional Convergence | p. 638 |
Maclaurin and Taylor Polynomials | p. 648 |
Maclaurin and Taylor Series; Power Series | p. 659 |
Convergence of Taylor Series | p. 668 |
Differentiating and Integrating Power Series; Modeling with Taylor Series | p. 678 |
Parametric And Polar Curves; Conic Sections | p. 692 |
Parametric Equations; Tangent Lines and Arc Length for Parametric Curves | p. 692 |
Polar Coordinates | p. 705 |
Tangent Lines, Arc Length, and Area for Polar Curves | p. 719 |
Conic Sections | p. 730 |
Rotation of Axes; Second-Degree Equations | p. 748 |
Conic Sections in Polar Coordinates 754 A APPENDICES A GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS A1 B TRIGONOMETRY REVIEW A13 C SOLVING POLYNOMIAL EQUATIONS A27 D SELECTED PROOFS A34 ANSWERS TO ODD-NUMBERED EXERCISES A45 | |
Index | p. I-1 |
Web Appendices (online only) | |
Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS | |
Real Numbers, Intervals, And Inequalities | |
Absolute Value | |
Coordinate Planes, Lines, And Linear Functions | |
Distance, Circles, And Quadratic Equations | |
Early Parametric Equations Option | |
Mathematical Models | |
The Discriminant | |
Second-Order Linear Homogeneous Differential Equations | |
Web Projects: Expanding the Calculus Horizon (online only) | |
Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS | |
Blammo The Human Cannonball | |
Comet Collision | |
Hurricane Modeling | |
Iteration And Dynamical Systems | |
Railroad Design | |
Robotics | |
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